What is the general solution for 4cos(θ)-2sqrt(3)=0 ?

The general solution for 4cos(θ)-2sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin

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4cos(θ)-2sqrt(3)=0

4 cos (θ) - 23 = 0

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

4 cos (θ) - 23 = 0

Move

23

to the right side

4 cos (θ) - 23 = 0

Add

23

to both sides

4 cos (θ) - 23 + 23 = 0 + 23

Simplify

4 cos (θ) = 23

4 cos (θ) = 23

Divide both sides by

4

4 cos (θ) = 23

Divide both sides by

4

\frac{4 cos ( θ )}{4} = \frac{2 3}{4}

Simplify

cos (θ) = \frac{3}{2}

cos (θ) = \frac{3}{2}

General solutions for

cos (θ) = \frac{3}{2}

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

\frac{3}{cot ( x )} = 8 - 5 tan (x)

sin (θ) = \frac{3}{8}, sin (2 θ)

2 (1 - cos^{2} (x)) = \frac{3}{2}

cos (3 θ) = - \frac{2}{2}

25 \cdot sin (x) - 1.5 \cdot cos (x) = 20

What is the general solution for 4cos(θ)-2sqrt(3)=0 ?
The general solution for 4cos(θ)-2sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin